%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP130-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:56:29 EDT 2022
% Result : Unsatisfiable 1.60s 1.83s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 11 unt; 11 nHn; 29 RR)
% Number of literals : 64 ( 0 equ; 19 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 29 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,e_1,B)
| product(A,e_2,B)
| product(A,e_3,B) ),
file('GRP130-4.003.p',unknown),
[] ).
cnf(3,axiom,
( product(A,B,C)
| ~ product(D,B,A)
| ~ product(A,C,D) ),
file('GRP130-4.003.p',unknown),
[] ).
cnf(4,axiom,
( product(A,B,C)
| ~ product(C,D,A)
| ~ product(A,D,B) ),
file('GRP130-4.003.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_1,e_2),
file('GRP130-4.003.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_2,e_1),
file('GRP130-4.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
file('GRP130-4.003.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP130-4.003.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP130-4.003.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(A,B,C)
| ~ product(A,C,D)
| product(D,B,A) ),
file('GRP130-4.003.p',unknown),
[] ).
cnf(17,plain,
( ~ group_element(A)
| product(A,e_1,A)
| product(A,e_2,A)
| product(A,e_3,A) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.2')] ).
cnf(18,plain,
( product(A,B,B)
| ~ product(A,B,A) ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.2.3')] ).
cnf(19,plain,
( product(A,A,A)
| ~ product(A,B,A) ),
inference(factor,[status(thm)],[4]),
[iquote('factor,4.2.3')] ).
cnf(25,axiom,
group_element(e_1),
file('GRP130-4.003.p',unknown),
[] ).
cnf(26,axiom,
group_element(e_2),
file('GRP130-4.003.p',unknown),
[] ).
cnf(29,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(hyper,[status(thm)],[25,17]),
[iquote('hyper,25,17')] ).
cnf(32,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_2) ),
inference(hyper,[status(thm)],[26,17]),
[iquote('hyper,26,17')] ).
cnf(34,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(hyper,[status(thm)],[26,11,25]),
[iquote('hyper,26,11,25')] ).
cnf(36,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(hyper,[status(thm)],[26,2,25]),
[iquote('hyper,26,2,25')] ).
cnf(63,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[29,19])]),
[iquote('hyper,29,19,factor_simp')] ).
cnf(70,plain,
product(e_1,e_1,e_1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[63,19])]),
[iquote('hyper,63,19,factor_simp')] ).
cnf(77,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_3,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[32,19])]),
[iquote('hyper,32,19,factor_simp')] ).
cnf(85,plain,
product(e_2,e_2,e_2),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[77,19])]),
[iquote('hyper,77,19,factor_simp')] ).
cnf(87,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[34,18])]),
[iquote('hyper,34,18,factor_simp')] ).
cnf(96,plain,
product(e_1,e_2,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[87,14,85]),7]),
[iquote('hyper,87,14,85,unit_del,7')] ).
cnf(102,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[36,12,70]),5]),
[iquote('hyper,36,12,70,unit_del,5')] ).
cnf(110,plain,
product(e_1,e_3,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[102,14,85]),7]),
[iquote('hyper,102,14,85,unit_del,7')] ).
cnf(113,plain,
product(e_2,e_2,e_1),
inference(hyper,[status(thm)],[110,15,96]),
[iquote('hyper,110,15,96')] ).
cnf(117,plain,
e_qualish(e_2,e_1),
inference(hyper,[status(thm)],[113,12,85]),
[iquote('hyper,113,12,85')] ).
cnf(118,plain,
$false,
inference(binary,[status(thm)],[117,7]),
[iquote('binary,117.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP130-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 04:47:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.60/1.83 ----- Otter 3.3f, August 2004 -----
% 1.60/1.83 The process was started by sandbox on n017.cluster.edu,
% 1.60/1.83 Wed Jul 27 04:47:18 2022
% 1.60/1.83 The command was "./otter". The process ID is 4445.
% 1.60/1.83
% 1.60/1.83 set(prolog_style_variables).
% 1.60/1.83 set(auto).
% 1.60/1.83 dependent: set(auto1).
% 1.60/1.83 dependent: set(process_input).
% 1.60/1.83 dependent: clear(print_kept).
% 1.60/1.83 dependent: clear(print_new_demod).
% 1.60/1.83 dependent: clear(print_back_demod).
% 1.60/1.83 dependent: clear(print_back_sub).
% 1.60/1.83 dependent: set(control_memory).
% 1.60/1.83 dependent: assign(max_mem, 12000).
% 1.60/1.83 dependent: assign(pick_given_ratio, 4).
% 1.60/1.83 dependent: assign(stats_level, 1).
% 1.60/1.83 dependent: assign(max_seconds, 10800).
% 1.60/1.83 clear(print_given).
% 1.60/1.83
% 1.60/1.83 list(usable).
% 1.60/1.83 0 [] -group_element(X)| -group_element(Y)|product(e_1,X,Y)|product(e_2,X,Y)|product(e_3,X,Y).
% 1.60/1.83 0 [] -group_element(X)| -group_element(Y)|product(X,e_1,Y)|product(X,e_2,Y)|product(X,e_3,Y).
% 1.60/1.83 0 [] product(X,Y,Z1)| -product(Z2,Y,X)| -product(X,Z1,Z2).
% 1.60/1.83 0 [] product(X,Z1,Z2)| -product(Z2,Y,X)| -product(X,Y,Z1).
% 1.60/1.83 0 [] group_element(e_1).
% 1.60/1.83 0 [] group_element(e_2).
% 1.60/1.83 0 [] group_element(e_3).
% 1.60/1.83 0 [] -e_qualish(e_1,e_2).
% 1.60/1.83 0 [] -e_qualish(e_1,e_3).
% 1.60/1.83 0 [] -e_qualish(e_2,e_1).
% 1.60/1.83 0 [] -e_qualish(e_2,e_3).
% 1.60/1.83 0 [] -e_qualish(e_3,e_1).
% 1.60/1.83 0 [] -e_qualish(e_3,e_2).
% 1.60/1.83 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 1.60/1.83 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.60/1.83 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.60/1.83 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.60/1.83 0 [] -product(X,Y,Z1)| -product(X,Z1,Z2)|product(Z2,Y,X).
% 1.60/1.83 end_of_list.
% 1.60/1.83
% 1.60/1.83 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.60/1.83
% 1.60/1.83 This is a non-Horn set without equality. The strategy will
% 1.60/1.83 be ordered hyper_res, unit deletion, and factoring, with
% 1.60/1.83 satellites in sos and with nuclei in usable.
% 1.60/1.83
% 1.60/1.83 dependent: set(hyper_res).
% 1.60/1.83 dependent: set(factor).
% 1.60/1.83 dependent: set(unit_deletion).
% 1.60/1.83
% 1.60/1.83 ------------> process usable:
% 1.60/1.83 ** KEPT (pick-wt=16): 1 [] -group_element(A)| -group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_3,A,B).
% 1.60/1.83 ** KEPT (pick-wt=16): 2 [] -group_element(A)| -group_element(B)|product(A,e_1,B)|product(A,e_2,B)|product(A,e_3,B).
% 1.60/1.83 ** KEPT (pick-wt=12): 3 [] product(A,B,C)| -product(D,B,A)| -product(A,C,D).
% 1.60/1.83 ** KEPT (pick-wt=12): 4 [] product(A,B,C)| -product(C,D,A)| -product(A,D,B).
% 1.60/1.83 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_1,e_2).
% 1.60/1.83 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_1,e_3).
% 1.60/1.83 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_2,e_1).
% 1.60/1.83 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_2,e_3).
% 1.60/1.83 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_1).
% 1.60/1.83 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_3,e_2).
% 1.60/1.83 ** KEPT (pick-wt=16): 11 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3).
% 1.60/1.83 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.60/1.83 ** KEPT (pick-wt=11): 13 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.60/1.83 ** KEPT (pick-wt=11): 14 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.60/1.83 ** KEPT (pick-wt=12): 15 [] -product(A,B,C)| -product(A,C,D)|product(D,B,A).
% 1.60/1.83
% 1.60/1.83 ------------> process sos:
% 1.60/1.83 ** KEPT (pick-wt=2): 25 [] group_element(e_1).
% 1.60/1.83 ** KEPT (pick-wt=2): 26 [] group_element(e_2).
% 1.60/1.83 ** KEPT (pick-wt=2): 27 [] group_element(e_3).
% 1.60/1.83
% 1.60/1.83 ======= end of input processing =======
% 1.60/1.83
% 1.60/1.83 =========== start of search ===========
% 1.60/1.83
% 1.60/1.83 -------- PROOF --------
% 1.60/1.83
% 1.60/1.83 ----> UNIT CONFLICT at 0.01 sec ----> 118 [binary,117.1,7.1] $F.
% 1.60/1.83
% 1.60/1.83 Length of proof is 17. Level of proof is 8.
% 1.60/1.83
% 1.60/1.83 ---------------- PROOF ----------------
% 1.60/1.83 % SZS status Unsatisfiable
% 1.60/1.83 % SZS output start Refutation
% See solution above
% 1.60/1.83 ------------ end of proof -------------
% 1.60/1.83
% 1.60/1.83
% 1.60/1.83 Search stopped by max_proofs option.
% 1.60/1.83
% 1.60/1.83
% 1.60/1.83 Search stopped by max_proofs option.
% 1.60/1.83
% 1.60/1.83 ============ end of search ============
% 1.60/1.83
% 1.60/1.83 -------------- statistics -------------
% 1.60/1.83 clauses given 25
% 1.60/1.83 clauses generated 895
% 1.60/1.83 clauses kept 117
% 1.60/1.83 clauses forward subsumed 796
% 1.60/1.83 clauses back subsumed 70
% 1.60/1.83 Kbytes malloced 976
% 1.60/1.83
% 1.60/1.83 ----------- times (seconds) -----------
% 1.60/1.83 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.60/1.83 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.60/1.83 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.60/1.83
% 1.60/1.83 That finishes the proof of the theorem.
% 1.60/1.83
% 1.60/1.83 Process 4445 finished Wed Jul 27 04:47:19 2022
% 1.60/1.83 Otter interrupted
% 1.60/1.83 PROOF FOUND
%------------------------------------------------------------------------------